MathDB
period of shuffling sequence

Source: IMOC 2019 C2

August 19, 2021
combinatorics

Problem Statement

For 2n2n numbers in a row, Bob could perform the following operation: Si=(a1,a2,…,a2n)↦Si+1=(a1,a3,…,a2n−1,a2,a4,…,a2n).S_i=(a_1,a_2,\ldots,a_{2n})\mapsto S_{i+1}=(a_1,a_3,\ldots,a_{2n-1},a_2,a_4,\ldots,a_{2n}). Let TT be the order of this operation. In other words, TT is the smallest positive integer such that Si=Si+TS_i=S_{i+T}. Prove that T<2nT<2n.
Back to ProblemsView on AoPS